{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FQXCS3OTY52I2FMQQ6EZSDB4NC","short_pith_number":"pith:FQXCS3OT","canonical_record":{"source":{"id":"1209.2570","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"cda7b07d8cf07b33cadad869df15e88137bf5270a2b0f88ae94b9e7cd9dc8f5f","abstract_canon_sha256":"6f0b20ce2f67257c16a4032b2c6aa92f96b416990032283ddbbf10625205142e"},"schema_version":"1.0"},"canonical_sha256":"2c2e296dd3c7748d15908789990c3c6888aeb1f0fca184382e8f69a172ef9ff2","source":{"kind":"arxiv","id":"1209.2570","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2570","created_at":"2026-05-18T01:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2570v3","created_at":"2026-05-18T01:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2570","created_at":"2026-05-18T01:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"FQXCS3OTY52I","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FQXCS3OTY52I2FMQ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FQXCS3OT","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FQXCS3OTY52I2FMQQ6EZSDB4NC","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2570","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"cda7b07d8cf07b33cadad869df15e88137bf5270a2b0f88ae94b9e7cd9dc8f5f","abstract_canon_sha256":"6f0b20ce2f67257c16a4032b2c6aa92f96b416990032283ddbbf10625205142e"},"schema_version":"1.0"},"canonical_sha256":"2c2e296dd3c7748d15908789990c3c6888aeb1f0fca184382e8f69a172ef9ff2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:30.031429Z","signature_b64":"0djNHad6cF152SyludOjpF9nP+ze3czJOkhashkXmHptaB1cbTdZELsQC4uMd5RJ137wyEkEea/7HDJFWHVKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c2e296dd3c7748d15908789990c3c6888aeb1f0fca184382e8f69a172ef9ff2","last_reissued_at":"2026-05-18T01:54:30.031009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:30.031009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2570","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aLOtHec2rLwpgCCaDZVdUvlH3XB5ESEzljbjed9JTkERx2UcxGul0m+AyM6DrPKTsgRne1Tlm2b2uSyqSSRCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:14:37.978969Z"},"content_sha256":"8e85582d4a6aa652f772b55df367ef1740700714bd7ae19afefa0c5baa7139a5","schema_version":"1.0","event_id":"sha256:8e85582d4a6aa652f772b55df367ef1740700714bd7ae19afefa0c5baa7139a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FQXCS3OTY52I2FMQQ6EZSDB4NC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic skew products of quadratic polynomials over circle expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Weixiao Shen, Wen Huang","submitted_at":"2012-09-12T11:30:25Z","abstract_excerpt":"We prove that a Viana map with an arbitrarily non-constant real analytic coupling function admits two positive Lyapunov exponents almost everywhere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2570","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDAnAQkTYht0nieQjijFlZcpjF2rM+0HgfonoVvbYHCAQBiRJPq48d7gtVIeDNYvzHfS8aB975JyASmBgVSLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:14:37.979687Z"},"content_sha256":"07c050d443c911505b604f2440c392863f7b56704c5d00a11c7f1099d4f2fe72","schema_version":"1.0","event_id":"sha256:07c050d443c911505b604f2440c392863f7b56704c5d00a11c7f1099d4f2fe72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQXCS3OTY52I2FMQQ6EZSDB4NC/bundle.json","state_url":"https://pith.science/pith/FQXCS3OTY52I2FMQQ6EZSDB4NC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQXCS3OTY52I2FMQQ6EZSDB4NC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T05:14:37Z","links":{"resolver":"https://pith.science/pith/FQXCS3OTY52I2FMQQ6EZSDB4NC","bundle":"https://pith.science/pith/FQXCS3OTY52I2FMQQ6EZSDB4NC/bundle.json","state":"https://pith.science/pith/FQXCS3OTY52I2FMQQ6EZSDB4NC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQXCS3OTY52I2FMQQ6EZSDB4NC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FQXCS3OTY52I2FMQQ6EZSDB4NC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6f0b20ce2f67257c16a4032b2c6aa92f96b416990032283ddbbf10625205142e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:30:25Z","title_canon_sha256":"cda7b07d8cf07b33cadad869df15e88137bf5270a2b0f88ae94b9e7cd9dc8f5f"},"schema_version":"1.0","source":{"id":"1209.2570","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2570","created_at":"2026-05-18T01:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2570v3","created_at":"2026-05-18T01:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2570","created_at":"2026-05-18T01:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"FQXCS3OTY52I","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FQXCS3OTY52I2FMQ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FQXCS3OT","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:07c050d443c911505b604f2440c392863f7b56704c5d00a11c7f1099d4f2fe72","target":"graph","created_at":"2026-05-18T01:54:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that a Viana map with an arbitrarily non-constant real analytic coupling function admits two positive Lyapunov exponents almost everywhere.","authors_text":"Weixiao Shen, Wen Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:30:25Z","title":"Analytic skew products of quadratic polynomials over circle expanding maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2570","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8e85582d4a6aa652f772b55df367ef1740700714bd7ae19afefa0c5baa7139a5","target":"record","created_at":"2026-05-18T01:54:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6f0b20ce2f67257c16a4032b2c6aa92f96b416990032283ddbbf10625205142e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:30:25Z","title_canon_sha256":"cda7b07d8cf07b33cadad869df15e88137bf5270a2b0f88ae94b9e7cd9dc8f5f"},"schema_version":"1.0","source":{"id":"1209.2570","kind":"arxiv","version":3}},"canonical_sha256":"2c2e296dd3c7748d15908789990c3c6888aeb1f0fca184382e8f69a172ef9ff2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c2e296dd3c7748d15908789990c3c6888aeb1f0fca184382e8f69a172ef9ff2","first_computed_at":"2026-05-18T01:54:30.031009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:30.031009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0djNHad6cF152SyludOjpF9nP+ze3czJOkhashkXmHptaB1cbTdZELsQC4uMd5RJ137wyEkEea/7HDJFWHVKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:30.031429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2570","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e85582d4a6aa652f772b55df367ef1740700714bd7ae19afefa0c5baa7139a5","sha256:07c050d443c911505b604f2440c392863f7b56704c5d00a11c7f1099d4f2fe72"],"state_sha256":"3fa127d2112457568b1781821603c77a46bd43c9215b92ddd2c663882af4cec4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UHn+cs7i41vB/BDVJiDqfBWcr6JAGxBKCnTe/qhtaWt2gPHP2+fNCaId/GG5NTngDgzK7G+Bj8zs+W2JMxSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:14:37.983331Z","bundle_sha256":"36710b3243ff161a2f6d8d2c127fbdf6c72451f364e2fc1805f57a800902f863"}}